Cañada, A.; Drábek, P. On semilinear problems with nonlinearities depending only on derivatives. (English) Zbl 0852.34018 SIAM J. Math. Anal. 27, No. 2, 543-557 (1996). The authors consider semilinear boundary value problems \[ u''(t)+ \lambda_1 u(t)+ g(t, u'(t))= f(t),\quad t\in I,\tag{1} \]\[ (Bu)(t)= 0,\quad t\in \partial I,\tag{2} \] where \(I= [0, \pi]\), \(B\) denotes either the Dirichlet or the Neumann or the periodic boundary conditions, respectively, and \(\lambda_1\) is the first eigenvalue of the corresponding linear problem \(u''(t)+ \lambda u(t)= 0\), \(t\in I\), \((Bu)(t)= 0\), \(t\in \partial I\). The nonlinear function \(g\) is supposed to be bounded and, in some cases, satisfies additional differentiability assumptions and asymptotic conditions. The authors emphasize the dependence of \(g\) on the derivative of the solution \(u'(t)\) in order to show the qualitative difference of this case and the Landesman-Lazer-type problem in which the nonlinearity \(g\) depends only on the solution \(u(t)\). The authors establish the solvability of the problem (1), (2). Reviewer: A.I.Kolosov (Khar’kov) Cited in 1 ReviewCited in 18 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations Keywords:semilinear boundary value problems; solvability PDF BibTeX XML Cite \textit{A. Cañada} and \textit{P. Drábek}, SIAM J. Math. Anal. 27, No. 2, 543--557 (1996; Zbl 0852.34018) Full Text: DOI OpenURL